There's a sense in which Lee Blessing's A Walk in the Woods is the ultimate park bench play – the customary two casual strangers replaced by a pair of nuclear arms negotiators (one from the US, the other from the Soviet Union) who meet for regular private conversations away from the official Geneva talks. The political climate has changed dramatically since the piece – inspired by an actual "walk in the woods" in the early 1980s when negotiators drafted their own breakthrough plan, soon to be rejected by both governments – was first seen in 1987. It's no longer a superpower stand-off that causes dread but our failure to stop the proliferation of nuclear weapons in small unstable regimes and, potentially, sub-national groups. Does this mean that the play is now looking dated?

Watching Nicolas Kent's accomplished production, which has transferred to the Tricycle from Northern Stage in Vermont, A Walk in the Woods now seems to be as much an existential as political drama. The new-broom idealism of American negotiator Joan Honeyman (all frowning seriousness and rubbery-mouthed persistence in Myriam Cyr's vivid performance) is brought up against the disconcerting playfulness and charm of Andrey Botvinnik (excellent Steven Crossley), a cynical veteran of the bargaining table, who wants to personalise their discussions with friendship and frivolity.

Blessing is light on the specifics of the official talks and heavy-handed with the odd-couple format (Joan's talent for carefree trivia is on a par with Mrs Thatcher's). But Botvinnik, with his gradually revealed disillusionment, powerfully expresses the existential predicament of the nuclear arms negotiator – doomed to failure because governments would only ever get rid of weapons built as bargaining chips in the first place. "There is the quest for the appearance of the quest for peace," he tells Joan, adding that it is not exactly pleasant to discover that playing complex, futile games is all that you were meant for.

A Walk in the Woods has a somewhat prefabricated feel and more than its fair share of clunky moments. But it persuasively shows two people who would have a better chance of success working as friends behind the backs of their manipulative, face-saving governments than as a Rosencrantz and Guildenstern on opposite sides of the table.